Can The Mystery of The Born-Oppenheimer Electronic Current Density Be Explained With A Simple Phase Space Electronic Hamiltonian? Yes (And A Lot More Too)

We show that a phase space electronic Hamiltonian $\hat{H}_{PS}(\mathbf{X},\mathbf{P})$, parameterized by both nuclear position $\mathbf{X}$ and momentum $\mathbf{P}$, can recover not just experimental vibrational circular dichroism (VCD) signals, but also a meaningful electronic current density that explains the features of the VCD rotatory strengths. Combined with earlier demonstrations that such Hamiltonians can also recover qualitatively correct electronic momenta with electronic densities that approximately satisfy a continuity equation, the data would suggest that we have isolated a meaningful alternative approach to electronic structure theory, one that entirely avoids Born-Oppenheimer theory and frozen nuclei. While the dynamical implications of such a phase space electronic Hamiltonian are not yet known, we hypothesize that, by offering classical trajectories the conserve the total angular momentum (unlike Born-Oppenheimer theory), this new phase space electronic structure Hamiltonian may well explain some fraction of the chiral-induced spin selectivity effect.